Properties

Label 1502.2.d
Level $1502$
Weight $2$
Character orbit 1502.d
Rep. character $\chi_{1502}(569,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $256$
Sturm bound $376$

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Defining parameters

Level: \( N \) \(=\) \( 1502 = 2 \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1502.d (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(376\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1502, [\chi])\).

Total New Old
Modular forms 760 256 504
Cusp forms 744 256 488
Eisenstein series 16 0 16

Trace form

\( 256 q + 4 q^{3} - 64 q^{4} - 4 q^{5} - 2 q^{6} - 12 q^{7} - 70 q^{9} + O(q^{10}) \) \( 256 q + 4 q^{3} - 64 q^{4} - 4 q^{5} - 2 q^{6} - 12 q^{7} - 70 q^{9} - 4 q^{10} - 6 q^{12} + 12 q^{13} - 4 q^{14} + 12 q^{15} - 64 q^{16} - 8 q^{17} - 16 q^{18} - 20 q^{19} - 4 q^{20} - 20 q^{21} - 6 q^{22} - 30 q^{23} - 2 q^{24} - 86 q^{25} - 12 q^{26} - 26 q^{27} - 2 q^{28} - 26 q^{29} + 6 q^{30} - 4 q^{31} + 30 q^{33} + 8 q^{34} - 20 q^{35} - 60 q^{36} + 8 q^{37} - 24 q^{38} - 8 q^{39} + 6 q^{40} + 64 q^{41} + 42 q^{42} - 32 q^{43} + 10 q^{44} - 4 q^{45} - 8 q^{46} + 8 q^{47} + 4 q^{48} - 108 q^{49} - 12 q^{50} + 40 q^{51} - 8 q^{52} + 20 q^{53} - 20 q^{54} - 46 q^{55} - 4 q^{56} - 10 q^{57} - 10 q^{58} - 46 q^{59} + 2 q^{60} - 52 q^{61} - 12 q^{62} - 18 q^{63} - 64 q^{64} + 40 q^{65} - 16 q^{66} - 20 q^{67} - 8 q^{68} - 68 q^{69} - 38 q^{70} + 42 q^{71} - 16 q^{72} + 108 q^{73} + 30 q^{74} - 86 q^{75} - 20 q^{76} + 58 q^{77} + 44 q^{78} + 24 q^{79} + 16 q^{80} - 2 q^{81} - 8 q^{82} + 152 q^{83} + 10 q^{84} + 72 q^{85} + 12 q^{86} + 16 q^{87} + 4 q^{88} + 54 q^{89} + 8 q^{90} - 74 q^{91} + 50 q^{92} + 132 q^{93} + 26 q^{94} - 70 q^{95} - 2 q^{96} - 34 q^{97} - 8 q^{98} + 128 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1502, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1502, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1502, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(751, [\chi])\)\(^{\oplus 2}\)